The Boom and Bust Cycles of Full Waveform
The Boom and Bust Cycles of Full Waveform Inversion: Is FWI a Bust, a Boom, or Becoming a Commodity? Gerard Schuster KAUST Dow Jones Index Avg/decade Normalized DJI 1. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s 2010 -2016
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples L 1 d 1 L 2 m = d 2 4. Summary
Medical vs Seismic Imaging CAT Scan MRI Full Waveform Inversion Tomogram
t t L L Vshallow = L/t Vdeep = L/t time Traveltime Tomogram & Migration Images
time Traveltime Tomogram & Migration Images Vshallow = L/t Intersection of down & up rays Vdeep = L/t
time Traveltime Tomogram & Migration Images Vshallow = L/t Vdeep = L/t
Traveltime Tomogram & Migration Images time Problems: Hi-Freq. ray tracing, picking traveltimes, tedious, Shot gather = d(x, t) low resolution, fails in complex earth models Vshallow = L/t migration image Vdeep = L/t
Full Waveform Inversion predicted traces Given: d(x, t) = Find: v(x, y, z) minimizes e=x, t S[d(x, t)-d(x, t)obs]2 Time predicted observed residual Problems: Hi-Freq. ray tracing, picking traveltimes, tedious, low resolution, fails in complex earth models - =
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples L 1 d 1 L 2 m = d 2 4. Summary
Gulf of Mexico Seismic Survey Predicted data 4 d 1 Time (s) L 1 m = d 1 L 2 m. = d 2 . . Observed data Goal: Solve overdetermined System of equations for m L N m = d. N 0 6 X (km) m
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples L 1 d 1 L 2 m = d 2 4. Summary
Details of Ldm = (k) T obs (k) dm = L (d-d ) obs d-d dobs Time (s) Reflectivity or velocity model [ – 1 d 2 ]d(g|s) = F c 2 dt 2 2 0 6 X (km) d(g|s) = [ 2 - 1 d 2 c 2 dt 2 ] Predicted data Observed data m -1 F
Conventional FWI Solution L d L= L & d = d 1 1 2 2 Given: Lm=d 2 Find: m s. t. min||Lm-d|| T -1 In general, huge dimension matrix T Solution: m = [L L] L d or if L is too big m = m – a L (Lm - d) = m – a [ L (L m - d ) + L (L m (k+1) (k) T (k) (k) T T 1 1 1 2 2 - d )] 2
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples L 1 d 1 L 2 m = d 2 4. Summary
Dow Jones Index vs FWI Index Dow Jones Industrial Avg/decade FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s Tarantola + French School 2000 s Bunks Multiscale Mora 2010 -2016 Exxon+ BP+Pratt
Dow Jones Index vs FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s 2010 -2016
What Caused the 1 st FWI Boom? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1990 s 2000 s 2010 -2016 FWI v(x, z) True v(x, z) 0 1980 s Z (km) 2 0 X (km) 4
What Caused the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1990 s 2000 s 2010 -2016 FWI v(x, z) True v(x, z) 0 1980 s Z (km) 2 0 X (km) 24
What Caused the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s 2010 -2016 predicted observed residual 1 5. 0 - ime (s) 0. 0 x =Waveform Misfit 0 Vtrue V Vstart
What Caused the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s 2010 -2016 predicted observed residual 1 5. 0 - ime (s) 0. 0 x =Waveform Misfit 0 Vtrue V Vstart
What Caused the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s predicted observed residual 1 5. 0 - ime (s) 0. 0 x 2000 s 2010 -2016 Gradient opt. gets stuck local minima =Waveform Misfit 0 Vtrue V Vstart
How to Cure the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s 2010 -2016 predicted observed residual 5. 0 Low-pass filter - ime (s) 0. 0 1 x ==Waveform Misfit Gradient opt global minima 0 Vstart Vtrue V
How to Cure the 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s predicted observed residual 5. 0 Window early events - ime (s) 0. 0 1 x 2000 s 2010 -2016 Multiscale FWI v(x, z) ==Waveform Misfit 0 Vtrue V Vstart
2004 EAGE Meeting New Boom How to Cure the. Started 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1980 s 1990 s 2000 s 2010 -2016 FWI v(x, z) Multiscale FWI v(x, z) True v(x, z) 0 1970 s Z (km) 2 0 X (km) 24
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples: Transmission FWI Norway L 1 d 1 L 2 m = d 2 4. Summary
Transmission 3 D FWI Norway Marine Data 2300 buried hydrophones, 50, 000 shots, sea bottom 70 m 16 km 8 km 4. 5 gas Gas cloud 1. 5 km/s 3. 5 km/s Small dimensions of structures such as sandy outwash channels to 175 m depth (Figure 1 c) and the scars left on the sea paleo-bottom by drifting icebergs to 500 m depth (Figure 1 d). A wide low speed region defines the geometry of the gas cloud (Figure 1 a, e) the periphery of which a fracture network is identified (Figure 1 b, S. Operto, A. Miniussi, R. Brossier, L. Combe, L. e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1 a, b, Metivier, V. Monteiller, Ribodetti A. , and J. white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes Virieux, 2015, GJI. penetration seismic wave.
Transmission 3 D FWI Norway Marine Data 2300 buried hydrophones, 50, 000 shots, sea bottom 70 m 16 km 8 km 4. 5 1. 5 km/s 3. 5 km/s
2 Transmission D FWI R+T 3 D Gulf of Mexico Marine. Data FWI Norway Marine 2300 buried hydrophones, 50, 000 shots, sea bottom 70 m Transmissions 10 x stronger than reflections Therefore gradients will spend greater effort updating shallow v(x, y, z) shallow V V Vdeep ? ? ?
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples: R+T FWI Gulf of Mexico L 1 d 1 L 2 m = d 2 4. Summary
2 D FWI R+T Gulf of Mexico Marine Data Transmission Cigars observed predicted Reflection Rabbit Ears predicted Abdullah Al. Theyab (2015)
2 D FWI R+T Gulf of Mexico Marine Data Transmission Cigars 0. 0 Z (km) observed predicted 3. 6 0. 0 X (km) Initial. V(x, z) Migration Image with FWI Abdullah Al. Theyab (2015) 19 Migration Image with FWI V(x, z)
Outline 1. Inversion Overview: 2. Seismic Experiment: L 1 m = d 1 L 2 m. = d 2 . . L N m = d. N 3. FWI, History, Examples: Phase FWI Surface Waves L 1 d 1 L 2 m = d 2 4. Summary
2 D KSA Potash Model Test True Model 0 30 0 60 x(m) z (m) 800 600 400 30 60 x(m) 30 400 w 0 120 60 x(m) 120 1 D Vs Tomogram m/s 0 0 600 120 WD Vs Tomogram 800 aves 600 e c a f 400 sur m/s z (m) 800 10 m Start Model m/s 0 800 z (m) 0 m/s 600 400 30 0 60 x(m) 120
Problem & Solution Problem: 1 D Dispersion inversion assumes layered medium (Xia et al. 1999). Solution: v(x, y, z) minimizes e=S[c(k, w)-c(k, w)obs]2 FWI: e=S[d(x, t)-d(x, t)obs]2 Dispersion Curves CSGs 60 x(m) 120 t(s) 0 x (m) Z (m) w(Hz) (Radon Transform) Dispersion Curves Radon 30 1 D WDVs Vs. Tomogram 00 2 D WD 1 D Inversion 30 30 v (m/s) Z (m) x (m) 1 D Inversion C (m/s) Z (m) t(s) 0 v (m/s) (m) ZZ (m) Radon C (m/s) CSGs True model (Li & Schuster, 2016) 0 w(Hz) 0 60 60 x(m) 120
Seismic Imaging of Olduvai Basin Kai Lu, Sherif Hanafy, Ian Stanistreet, Jackson Njau, Kathy Schick , Nicholas Toth and Gerard Schuster
Olduvai, Tanzania Seismic Data The Fifth Fault COG z (m) 0 0. 6 0 500 1000 The Fifth Fault 1500 2000 2500 3000 3500 S-wave Velocity Tomogram (WD) m/s 0 z (m) 1000 800 0. 6 600 0 500 1000 The Fifth Fault 2000 2500 3000 P-wave Velocity Tomogram 3500 m/s 3500 z (m) 0 1500 2000 1500 0. 6 0 500 1000 1500 2000 2500 3000 3500
Summary 1. Multiscale+Skeletonized FWI: e =Si |di –di pred |2 v(x, y, z), r(x, y, z) 2. History 1930 s 1980 1990 2010 -2016 3. Is FWI a commodity? Almost according to 2 industry experts Is FWI a black box? Not yet, works ~80% time (2 experts) Challenges? Deeper imaging, CPU cost, multiparameter
Summary 4. Road Ahead 3 D Elastic Inversion & Adaptive Grid. Worth it? 3 D Viscoelastic Inversion. Worth it? Clever Skeletonized FWI Anisotropic Inversion Multiples? ? Inversion Deeper than src-rec offset/depth<2
Summary (We need faster migration algorithms & better velocity models) Stnd. FWI Multsrc. FWI IO 1 vs 1/20 or better Cost 1 vs 1/20 Sig/Mults. Sig Resolution dx ? 1 vs 1 or better
Qademah Fault, Saudi Arabia Field Data P-wave Tomogram 2 D WD S-wave Tomogram 1 D S-wave Tomogram
Comparison of 2 D WD Inversion with FWI Start Model FWI of Surface Waves Easy to get stuck in a local minimum (Solano, et al. , 2014). Vs True Model Vs Tomogram A shot gather FWI z (m) t (s) z (m) FD x (m) 2 D WD of Surface Waves Avoid local minimum and apply in 2 D/3 D model. Vs Tomogram Dispersion curve x (m) z (m) t (s) v (m/s) WD f (Hz) x (m)
2004 EAGE Meeting New Boom How to Cure the. Started 1 st FWI Bust? FWI Index Avg/decade 18. 0 0. 0 1930 s 1940 s 1950 s 1960 s 1980 s 1990 s 2000 s 2010 -2016 FWI v(x, z) Multiscale FWI v(x, z) True v(x, z) 0 1970 s Z (km) 2 0 X (km) 24
Full Waveform Inversion time Given: d(x, t) = Find: v(x, y, z) minimizes e=x, t. S[d(x, t)-d(x, t)obs]2 Vshallow = L/t migration image Vdeep = L/t
Transmission 3 D FWI Norway Marine Data 2300 buried hydrophones, 50, 000 shots, sea bottom 70 m 16 km 8 km 4. 5 gas Gas cloud 1. 5 km/s 3. 5 km/s Small dimensions of structures such as sandy outwash channels to 175 m depth (Figure 1 c) and the scars left on the sea paleo-bottom by drifting icebergs to 500 m depth (Figure 1 d). A wide low speed region defines the geometry of the gas cloud (Figure 1 a, e) the periphery of which a fracture network is identified (Figure 1 b, S. Operto, A. Miniussi, R. Brossier, L. Combe, L. e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1 a, b, Metivier, V. Monteiller, Ribodetti A. , and J. white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes Virieux, 2015, GJI. penetration seismic wave.
- Slides: 44